如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB……急需!如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB,交AD于点E,CF=4cm.(1)求

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如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB……急需!如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB,交AD于点E,CF=4cm.(1)求
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如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB……急需!如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB,交AD于点E,CF=4cm.(1)求
如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB……急需!
如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB,交AD于点E,CF=4cm.
(1)求证:四边形ABFE是等腰梯形;
(2)求AB的长.

如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB……急需!如图,在直角梯形ABCD中,AB∥DC,∠ABC=90°,AB=2DC,对角线AC⊥BD,垂足为F,过点F作EF∥AB,交AD于点E,CF=4cm.(1)求
⑴过D点作AB的垂线,垂足为H点,则四边形DHBC是矩形,∴BH=DC,设DC=x,则HB=x,∴AH=x,∴H是AB中点,∴△DAB是等腰△,即DA=DB,又∵EF∥AB,则EA=FB,∴四边形ABFE是等腰梯形.⑵设DF=y,则由DC∥AB得:△DCF∽△BAF,∴BF=2y,CF=4,则AF=8,∴由勾股定理得:①CF²+BF²=CB²=DB²-HB²,即:4²+﹙2y﹚²=﹙3y﹚²-x²,整理得:5y²-x²=16,②DF²+CF²=DC²,即y²+4²=x²,联合①②解得:x=2√6,y=2√2,∴AB=2x=4√6